The subject matter described herein relates generally to satellite systems and, more particularly, to methods and systems for controlling a plurality of satellites using node-synchronous eccentricity control.
Spacecraft, such as satellites, are placed in Earth orbits for a variety of purposes, e.g., weather monitoring, scientific observations and commercial communications. Accordingly, they are maintained in a variety of attitudes and placed in a variety of orbits (e.g., low Earth orbit, transfer orbit, inclined geosynchronous orbit and geostationary orbit).
At geosynchronous orbit, a spacecraft's orbital position is typically defined by the orbit's eccentricity, the inclination of the orbital plane from the Earth's equatorial plane, and the spacecraft's longitude. In a geostationary orbit, the spacecraft's orbital period matches the Earth's rotational period, the eccentricity is substantially zero and the spacecraft's orbital plane is substantially coplanar with the Earth's equatorial plane. The principal forces which disturb a spacecraft's position are generated by the gravity of the sun and the moon, the Earth's elliptical shape (triaxiality) and solar radiation pressure.
Inclined geosynchronous orbits, which are often used for communications to mobile customers are similar to those of geostationary orbits, except, they have a non-zero inclination typically in the range of three to seven degrees. Such satellites pass through the equatorial plane twice each day, once at an ascending node (the portion of the satellite orbit above an equatorial plane), and once at a descending node (the portion of the satellite orbit below an equatorial plane). The motion of satellites in inclined geosynchronous orbits is more complex in practice, due to orbit eccentricity, drift and other perturbing forces.
Due to satellite-to-satellite communication interference issues, satellites in geostationary orbits are assigned to geostationary “slots” that may vary from 0.2 degrees wide to 0.1 degrees wide in longitude near the equatorial plane. Despite their motion, interference is still a problem, and satellites in inclined geosynchronous orbits are also assigned to geostationary “slots” near the equatorial plane, with the same constraints between 0.1 degrees and 0.2 degrees in longitude. These longitude constraints are typically defined in a latitude range of between 0.1 degrees and 0.2 degrees in the equatorial zone. The constraints in latitude and longitude, are sometimes referred to as defining a “box”.
The processes of maintaining a spacecraft's position with respect to the Earth and a position within the above described “slot” and/or “box” is generally referred to as stationkeeping. Stationkeeping may be facilitated with thrusters which are directed to generate forces through the spacecraft's center of mass. Attitude control is generally facilitated with momentum and/or reaction wheels whose momentum is periodically “dumped” when the same (or different) thrusters are directed to generate turning moments about the spacecraft's center of mass. Conventional thruster systems typically have sets of thrusters that are aligned in north-south and east-west directions. The north-south thrusters produce north-south velocity changes (ΔV) to control inclination. The east-west thrusters produce an east-west ΔV to control drift (change of longitude with time) and eccentricity.
The problem associated with maintaining a slot and/or box position is especially critical for current and future generation spacecraft. Such spacecraft often have large solar arrays and solar collectors, and therefore receive a strong solar force. This solar force requires a large steady state eccentricity when a single burn sun-synchronous perigee stationkeeping strategy is used. This eccentricity is difficult to control efficiently, even when a sun-synchronous perigee stationkeeping strategy, which compresses eccentricity using double burn control maneuvers, is used. In some satellites, the east/west longitude excursion due to eccentricity can take up more than half the width of the slot. Other factors also consume slot width, including drift over the maneuver cycle, maneuver execution error, ΔV increments associated with momentum dumping disturbances, orbit determination error, and orbit propagation error.
Maintaining a longitudinal position of such a satellite in a geosynchronous inclined orbit is sometimes referred to as east-west stationkeeping. Maintaining the inclination of the orbit is sometimes referred to as north-south station keeping. Maintaining the longitudinal position of satellites in a geosynchronous inclined orbit has been previously performed based on the sun-synchronous strategy introduced above. The sun-synchronous strategy was developed for use with near stationary orbits having near zero inclination. However, north-south stationkeeping is not required for most mobile communications satellites, which typically have larger inclinations over their lifespan, for example, between three and seven degrees over the life of the satellite.